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Full text of "Mathematical And Physical Papers - Iii"

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except No. 21, for which only two pair were performed. The following are the results. For the 1^-inch platina sphere 0*0644, mean error 0'0044. For the 1^-inch brass sphere 0*180, mean error 0*024. For the 2-inch brass sphere 0*094, mean error 0'013. For the copper rod 0*486, mean error 0*113. For the brass tube the results were 0145, 0*363, 0'338, 0*305. Rejecting the first result as anomalous, and taking the mean of the others, we get 0'335; mean error O'OSO. To obtain I from the mean results above given we have only to divide by 3600 times the modulus, and multiply by r, and for the experiments with spheres we may suppose T = 1.
The mode of calculating I from theory in the case of a sphere suspended by a fine wire has already been ex/plained. For the sake of exhibiting separately the effect of the wire, I will give one intermediate step in the calculation.
1-44 inch     1-46 inch      2-06 inch sphere.         sphere.         sphere.
A?', for sphere alone   ...............      O326        0*320        0*220
AJfe', the correction for the wire        0130        0130        0'045
Total, to be substituted in (169)      0'456        0*450        0'265
The formula (168), which applies to a sphere suspended by a wire, will be applicable to a long cylindrical rod if we suppose M = 0. Hence the same formula (169) that has been used for a sphere may be applied to a cylindrical rod if we suppose k' to refer to the rod. For the copper rod k'  1*107, and for the tube &'== 0*2561. The following are the results for the three spheres and two cylinders.
No. 1.       No. 3.      No. 6.     No. 21.      3538.
1000000 1, from experiment    41        115        60        315        206 ............   from theory......    39        106        60        237        156
Difference.........   +2        +9         0      +78      +50
It appears that the experiments with spheres are satisfied almost exactly. The differences between the results of theory and observation are much larger in the case of the long cylinders. Large as these differences appear, they are hardly beyond the limits of errors of observation, though they would probably be far beyond the limits of errors of observation in a set of experiments